Consider the function f : R³ → R defined byf(x, y, z) = tanh(5x² + 2y² - 3z²)and the point P: (x, y, z) = (1, 1, 1).(a) In what direction is f most rapidly increasing at the point P?(b) Calculate the directional derivative of f in the direction of u = (2, -1, 2) at the point P.(c) Determine an expression for the linear approximation f of f at point P.(d) Use the linear approximation to approximate the value of f(-).

Answered: Image /qna-images/answer/362e80be-fda4-4353-818a-f0664dc9716d.jpg

Answered: Consider the function f : R³ R defined…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.2: Partial Derivatives

Problem 25E

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